Problem: $ C = \left[\begin{array}{rrr}-2 & 3 & 1 \\ 4 & -1 & -2\end{array}\right]$ $ A = \left[\begin{array}{rr}-1 & 4 \\ 1 & 0 \\ 4 & 4\end{array}\right]$ Is $ C A$ defined?
Solution: In order for multiplication of two matrices to be defined, the two inner dimensions must be equal. If the two matrices have dimensions $( m \times  n)$ and $( p \times q)$ , then $ n$ (number of columns in the first matrix) must equal $ p$ (number of rows in the second matrix) for their product to be defined. How many columns does the first matrix, $ C$ , have? How many rows does the second matrix, $ A$ , have? Since $ C$ has the same number of columns (3) as $ A$ has rows (3), $ C A$ is defined.